Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Express the given complex number (-3) in the polar form.

Express the given complex number (-3) in the polar form.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5965 Points
one year ago
Welcome to AskIITians

Given, complex number is -3.

Let r cos θ = -3 …(1)

and r sin θ = 0 …(2)

Squaring and adding (1) and (2), we get

r2cos2θ + r2sin2θ = (-3)2

Take r2outside from L.H.S, we get

r2(cos2θ + sin2θ) = 9

We know that, cos2θ + sin2θ = 1, then the above equation becomes,

r2= 9

r = 3 (Conventionally, r > 0)

Now, subsbtitute the value of r in (1) and (2)

3 cos θ = -3 and 3 sin θ = 0

cos θ = -1 and sin θ = 0

Therefore, θ = π

Hence, the polar representation is,

-3 = r cos θ + i r sin θ

3 cos π + 3 sin π = 3(cos π + i sin π)

Thus, the required polar form is 3 cos π+ 3i sin π = 3(cos π+i sin π)

Thanks

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free